The temperature dependence of the frequencies of a Bose-Einstein condensate
obtained in experiment has not been fully understood theoretically. In thi
s paper we present a simplified version of a two-gas model. The ground stat
e of the system found numerically is used for small oscillation analysis. I
n the case of spherical symmetry a full spectrum of frequencies is found fo
r low orbital quantum numbers. Avoided crossings that appear in the spectru
m might be the reason for experimentally observed frequency shifts.